Shaking Force Balance of the Peaucellier-Lipkin Straight-Line Linkage

摘要

This paper shows three different approaches for the shaking force balancing of the Peaucellier-Lipkin straight-line linkage. First the common approach to balance a linkage by modeling one link in each closed loop with two equivalent masses and subsequently adding countermasses is shown, requiring five countermasses in total. With the second approach the parallelogram in the Peaucellier-Lipkin straightline linkage is considered a balanced pantograph with which three countermasses are required in total. The third approach consists of considering the parallelogram a mass-equivalent linkage for which the results only require two countermasses. It is also shown how with the second approach shaking force balance in a single direction is obtained by balancing the linkage about the joint tracing the straight line with only two counter-masses. All solutions are also statically balanced.